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There is a huge gulf between being able to follow a thought path and being able to find it oneself. I couldn't do the same work in the same timescale as them, I wouldn't make the same decisions or spot the same pitfalls. I am simply not as good. But I spent a bunch of pub/work time discussing it and could project an aura of authority on the projects if I wished.

Look at it this way. I was able to understand all of the maths proofs taught at my degree, but I could not have come up with them myself.

Yeah, that's a great analogy for the core problem.

Imagine putting a math problem in front of someone and asking them to solve it. They correctly identify it as a system of linear equations. They volunteer that they would solve it using x algorithm which has a time complexity of y.

Then you ask them to actually solve it, and they can't even make the first movement towards doing so. They mentioned LU decomposition, but they can't even do Gaussian elimination on paper. They don't know what elementary row operations are. They can't obtain an augmented matrix or put it into (reduced) row echelon form. They don't know anything about linear independence or the rank of a matrix. You put an inconsistent system in front of them and they keep banging away at it, determined to find a solution...etc.

That's what it's like interviewing one of these senior engineers. It's surreal - they confidently pattern match the problem using limited heuristics, and they toss away low hanging fruit to demonstrate knowledge. But when you ask them to do something practical and specific, they either refuse and zoom out into abstract-land again, or they hopelessly fail.

so for data scientists I guess you could ask them to hand calculate the variance and standard deviation for a sample and see how they do on that

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